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Mathematics, Volume 10, Issue 16 (August-2 2022) – 204 articles

Cover Story (view full-size image): Riemannian geometry was first put forward in generality by Bernhard Riemann in the 19th century. In turn, Solomon Hadamard made significant contributions to Riemannian differential geometry and partial differential equations. The following theorem bearing his name is well known: A complete, simply connected Riemannian manifold of nonpositive sectional curvature is diffeomorphic to the Euclidean space. Therefore, it is called a Hadamard manifold. The generalizations of Riemannian manifolds were used by Albert Einstein in the General Theory of Relativity. In our article, we prove several Liouville-type theorems for isometric and harmonic self-diffeomorphisms of Hadamard manifolds, as well as Liouville-type theorems for Killing-Yano, symmetric Killing and harmonic tensors on Hadamard manifolds. View this paper
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Article
Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method
Mathematics 2022, 10(16), 3028; https://doi.org/10.3390/math10163028 - 22 Aug 2022
Viewed by 339
Abstract
In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated [...] Read more.
In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated least squares algorithm. The basic concept is to remove the imposed bias by including a correction term into the least squares estimations. The suggested approach makes a significant contribution by the estimation, iteratively, of fractional order system coefficients as well as the orders and the time-delay using a nonlinear optimization algorithm. The main advantage of this method is to provide a simple and powerful algorithm with good accuracy. The suggest method performances are assessed through two numerical examples. Full article
(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)
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Article
Optimization of Open Queuing Networks with Batch Services
Mathematics 2022, 10(16), 3027; https://doi.org/10.3390/math10163027 - 22 Aug 2022
Viewed by 296
Abstract
In this paper, open queuing networks with Poisson arrivals and single-server infinite buffer queues are considered. Unlike traditional queuing models, customers are served (with exponential service time) in batches, so that the nodes are non-work-conserving. The main contribution of this work is the [...] Read more.
In this paper, open queuing networks with Poisson arrivals and single-server infinite buffer queues are considered. Unlike traditional queuing models, customers are served (with exponential service time) in batches, so that the nodes are non-work-conserving. The main contribution of this work is the design of an efficient algorithm to find the batch sizes which minimize the average response time of the network. As preliminary steps at the basis of the proposed algorithm, an analytical expression of the average sojourn time in each node is derived, and it is shown that this function, depending on the batch size, has a single minimum. The goodness of the proposed algorithm and analytical formula were verified through a discrete-event simulation for an open network with a non-tree structure. Full article
(This article belongs to the Special Issue Advances in Queueing Theory)
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Article
Tail Index Estimation of PageRanks in Evolving Random Graphs
Mathematics 2022, 10(16), 3026; https://doi.org/10.3390/math10163026 - 22 Aug 2022
Viewed by 305
Abstract
Random graphs are subject to the heterogeneities of the distributions of node indices and their dependence structures. Superstar nodes to which a large proportion of nodes attach in the evolving graphs are considered. In the present paper, a statistical analysis of the extremal [...] Read more.
Random graphs are subject to the heterogeneities of the distributions of node indices and their dependence structures. Superstar nodes to which a large proportion of nodes attach in the evolving graphs are considered. In the present paper, a statistical analysis of the extremal part of random graphs is considered. We used the extreme value theory regarding sums and maxima of non-stationary random length sequences to evaluate the tail index of the PageRanks and max-linear models of superstar nodes in the evolving graphs where existing nodes or edges can be deleted or not. The evolution is provided by a linear preferential attachment. Our approach is based on the analysis of maxima and sums of the node PageRanks over communities (block maxima and block sums), which can be independent or weakly dependent random variables. By an empirical study, it was found that tail indices of the block maxima and block sums are close to the minimum tail index of representative series extracted from the communities. The tail indices are estimated by data of simulated graphs. Full article
(This article belongs to the Special Issue New Advances and Applications of Extreme Value Theory)
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Article
A Refined Closed-Form Solution for Laterally Loaded Circular Membranes in Frictionless Contact with Rigid Flat Plates: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation
Mathematics 2022, 10(16), 3025; https://doi.org/10.3390/math10163025 - 22 Aug 2022
Cited by 1 | Viewed by 263
Abstract
Essential to the design and development of circular contact mode capacitive pressure sensors is the ability to accurately predict the contact radius, maximum stress, and shape of a laterally loaded circular membrane in frictionless contact with a concentric circular rigid flat plate. In [...] Read more.
Essential to the design and development of circular contact mode capacitive pressure sensors is the ability to accurately predict the contact radius, maximum stress, and shape of a laterally loaded circular membrane in frictionless contact with a concentric circular rigid flat plate. In this paper, this plate/membrane contact problem is solved analytically again by simultaneously improving both out-of-plane equilibrium equation and geometric equation, and a new and more refined closed-form solution is given to meet the need of accurate prediction. The new closed-form solution is numerically discussed in convergence and effectiveness and compared with the previous one, showing that it can greatly improve the prediction accuracy of the contact radius, maximum stress, and shape of the circular membrane in frictionless contact with the rigid flat plate. Full article
(This article belongs to the Special Issue Mathematics and Its Applications in Science and Engineering II)
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Article
Complexity-Efficient Coherent Physical Cell Identity Detection Method for Cellular IoT Systems
Mathematics 2022, 10(16), 3024; https://doi.org/10.3390/math10163024 - 22 Aug 2022
Viewed by 319
Abstract
Narrowband Internet of Things (NB-IoT) is one of the low-power wide-area network technologies that aim to support enormous connection, deep coverage, low power consumption, and low cost. Therefore, low cost of implementation and maintenance is one of the key challenges of NB-IoT terminals. [...] Read more.
Narrowband Internet of Things (NB-IoT) is one of the low-power wide-area network technologies that aim to support enormous connection, deep coverage, low power consumption, and low cost. Therefore, low cost of implementation and maintenance is one of the key challenges of NB-IoT terminals. This paper presents a low-complexity formulation for narrowband secondary synchronization signal (NSSS) detection in the NB-IoT system, supported by a coherent algorithm that requires a priori knowledge of the channel. By exploiting a symmetric conjugate feature of the NSSS sequence, a joint physical cell ID and radio frame number detection method with low complexity is proposed for coherent detection. The probability of erroneous detection of the presented NSSS detection method is computed, and the analytical model is verified by means of simulation. Numerical experiments will demonstrate that the proposed detection scheme remarkably reduces the computational complexity with almost the same detection ability compared to the existing detection scheme. Full article
(This article belongs to the Section Engineering Mathematics)
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Review
Review of Methods, Applications and Publications on the Approximation of Piecewise Linear and Generalized Functions
Mathematics 2022, 10(16), 3023; https://doi.org/10.3390/math10163023 - 22 Aug 2022
Cited by 1 | Viewed by 267
Abstract
Approximation of piecewise linear and generalized functions is an important and difficult problem. These functions are widely used in mathematical modeling of various processes and systems, such as: automatic control theory, electrical engineering, radio engineering, information theory and transmission of signals and images, [...] Read more.
Approximation of piecewise linear and generalized functions is an important and difficult problem. These functions are widely used in mathematical modeling of various processes and systems, such as: automatic control theory, electrical engineering, radio engineering, information theory and transmission of signals and images, equations of mathematical physics, oscillation theory, differential equations and many others. The widespread use of such functions is explained by their positive properties. For example, piecewise linear functions are characterized by a simple structure over segments. However, these features also have disadvantages. For example, in the case of using piecewise linear functions, solutions have to be built in segments. In this case, the problem of matching the obtained solutions at the boundaries of the segments arises, which leads to the complication of the research results. The use of generic functions has similar disadvantages. To eliminate shortcomings in practice, one resorts to the approximation of these functions. There are a large number of well-known methods for approximating piecewise linear and generalized functions. Recently, new methods for their approximation have been developed. In this study, an attempt was made to generalize and discuss the existing methods for approximating the considered functions. Particular emphasis is placed on the description of new approximation methods and their applications in various fields of science and technology. The publication-based review discusses the strengths and weaknesses of each method, compares them, and considers suitable application examples. The review will undoubtedly be interesting not only for mathematicians, but also for specialists and scientists working in various applied fields of research. Full article
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Article
Numerical Analyses and a Nonlinear Composite Controller for a Real-Time Ground Aerodynamic Heating Simulation of a Hypersonic Flying Object
Mathematics 2022, 10(16), 3022; https://doi.org/10.3390/math10163022 - 22 Aug 2022
Viewed by 273
Abstract
This paper contains two parts: numerical analyses and a control method. The numerical analyses of a hypersonic flying object’s aerodynamic heating environment are based on three different two-dimensional outflow fields via finite element calculations. Then, the reference temperature trajectories of a hypersonic flying [...] Read more.
This paper contains two parts: numerical analyses and a control method. The numerical analyses of a hypersonic flying object’s aerodynamic heating environment are based on three different two-dimensional outflow fields via finite element calculations. Then, the reference temperature trajectories of a hypersonic flying object are obtained. The other one is an intelligent proportional-derivative (IPD) with a nonlinear global sliding mode control (NGSMC) based on a nonlinear extended state observer (NESO) for a real-time ground aerodynamic heating simulation of a hypersonic flying object, named a thermal-structural test with quartz lamp heaters. The composite controller is made of three sub-components: a model free frame that is independent of the system dynamic model along with an ultra-local model; a NESO for the lumped disturbances observation; and an integral sliding mode control with a nonlinear function for the observation errors compensation. The flight environment of the hypersonic flying object is from Mach number 0.6 to Mach number 5.0, with between flight altitude of 31,272 m and flight altitude of 13,577 m. The comparative results demonstrate some superiorities of the proposed composite controller in terms of tracking errors and robustness. Full article
(This article belongs to the Section Engineering Mathematics)
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Article
Influence of the Algorithmization Process on the Mathematical Competence: A Case Study of Trainee Teachers Assessing ABN- and CBC-Instructed Schoolchildren by Gamification
Mathematics 2022, 10(16), 3021; https://doi.org/10.3390/math10163021 - 22 Aug 2022
Viewed by 307
Abstract
In this manuscript, schoolchild mathematical competencies have been assessed by using educational gamification methodologies; specifically, Educational Escape Rooms (EER). To ease the interpretation of results, Spanish schoolchildren trained by using two different methodologies (ABN and CBC) were selected to participate in the experience. [...] Read more.
In this manuscript, schoolchild mathematical competencies have been assessed by using educational gamification methodologies; specifically, Educational Escape Rooms (EER). To ease the interpretation of results, Spanish schoolchildren trained by using two different methodologies (ABN and CBC) were selected to participate in the experience. The gamified environment used as assessment tool was co-designed by trainee teachers, on-service teachers, and university researchers. The design was implemented in different educational centers and the results were transcribed to deliver a didactic analysis. Among the findings of this study, we uncovered: (i) the reduction of the math anxiety, (ii) the different performance of the schoolchild involved—ABN students show an additional and positive 10% development of certain mathematical competences—and (iii) a positive didactic-mathematic development of the participant trainee teachers. Full article
(This article belongs to the Section Engineering Mathematics)
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Article
A Fractional Order Model to Study the Effectiveness of Government Measures and Public Behaviours in COVID-19 Pandemic
Mathematics 2022, 10(16), 3020; https://doi.org/10.3390/math10163020 - 22 Aug 2022
Cited by 1 | Viewed by 266
Abstract
In this work, we emphasise the dynamical study of spreading COVID-19 in Bangladesh. Considering the uncertainty caused by the limited coronavirus (COVID-19) information, we have taken the modified Susceptible-Asymptomatic-Infectious-Hospitalised-Recovered (SAIHR) compartmental model in a Caputo fractional order system. We have also introduced public [...] Read more.
In this work, we emphasise the dynamical study of spreading COVID-19 in Bangladesh. Considering the uncertainty caused by the limited coronavirus (COVID-19) information, we have taken the modified Susceptible-Asymptomatic-Infectious-Hospitalised-Recovered (SAIHR) compartmental model in a Caputo fractional order system. We have also introduced public behavioural and government policy dynamics in our model. The dynamical nature of the solutions of the system is analysed and we have also calculated the sensitivity index of different parameters. It has been observed that public behaviour and government measures play an important role in controlling the pandemic situation. The government measures (social distance, vaccination, hospitalisation, awareness programme) are more helpful than only public responses to the eradication of the COVID-19 pandemic. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)
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Article
A Hybrid Sparrow Search Algorithm of the Hyperparameter Optimization in Deep Learning
Mathematics 2022, 10(16), 3019; https://doi.org/10.3390/math10163019 - 22 Aug 2022
Viewed by 311
Abstract
Deep learning has been widely used in different fields such as computer vision and speech processing. The performance of deep learning algorithms is greatly affected by their hyperparameters. For complex machine learning models such as deep neural networks, it is difficult to determine [...] Read more.
Deep learning has been widely used in different fields such as computer vision and speech processing. The performance of deep learning algorithms is greatly affected by their hyperparameters. For complex machine learning models such as deep neural networks, it is difficult to determine their hyperparameters. In addition, existing hyperparameter optimization algorithms easily converge to a local optimal solution. This paper proposes a method for hyperparameter optimization that combines the Sparrow Search Algorithm and Particle Swarm Optimization, called the Hybrid Sparrow Search Algorithm. This method takes advantages of avoiding the local optimal solution in the Sparrow Search Algorithm and the search efficiency of Particle Swarm Optimization to achieve global optimization. Experiments verified the proposed algorithm in simple and complex networks. The results show that the Hybrid Sparrow Search Algorithm has the strong global search capability to avoid local optimal solutions and satisfactory search efficiency in both low and high-dimensional spaces. The proposed method provides a new solution for hyperparameter optimization problems in deep learning models. Full article
(This article belongs to the Section Engineering Mathematics)
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Article
On the Conditional Value at Risk Based on the Laplace Distribution with Application in GARCH Model
Mathematics 2022, 10(16), 3018; https://doi.org/10.3390/math10163018 - 22 Aug 2022
Viewed by 309
Abstract
In this article, the Laplace distribution is employed in lieu of the well-known normal distribution for finding better scalar values of risk. Explicit formulas for value-at-risk (VaR) and conditional value-at-risk (CVaR) are studied and used to manage the risk involved in a stock [...] Read more.
In this article, the Laplace distribution is employed in lieu of the well-known normal distribution for finding better scalar values of risk. Explicit formulas for value-at-risk (VaR) and conditional value-at-risk (CVaR) are studied and used to manage the risk involved in a stock movement by using the GARCH model. Numerical simulations are given for a variety of stocks in equity markets to uphold the findings. Full article
(This article belongs to the Special Issue Numerical Analysis and Modeling)
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Review
Reinforcement Learning-Based Routing Protocols in Flying Ad Hoc Networks (FANET): A Review
Mathematics 2022, 10(16), 3017; https://doi.org/10.3390/math10163017 - 22 Aug 2022
Viewed by 421
Abstract
In recent years, flying ad hoc networks have attracted the attention of many researchers in industry and universities due to easy deployment, proper operational costs, and diverse applications. Designing an efficient routing protocol is challenging due to unique characteristics of these networks such [...] Read more.
In recent years, flying ad hoc networks have attracted the attention of many researchers in industry and universities due to easy deployment, proper operational costs, and diverse applications. Designing an efficient routing protocol is challenging due to unique characteristics of these networks such as very fast motion of nodes, frequent changes of topology, and low density. Routing protocols determine how to provide communications between drones in a wireless ad hoc network. Today, reinforcement learning (RL) provides powerful solutions to solve the existing problems in the routing protocols, and designs autonomous, adaptive, and self-learning routing protocols. The main purpose of these routing protocols is to ensure a stable routing solution with low delay and minimum energy consumption. In this paper, the reinforcement learning-based routing methods in FANET are surveyed and studied. Initially, reinforcement learning, the Markov decision process (MDP), and reinforcement learning algorithms are briefly described. Then, flying ad hoc networks, various types of drones, and their applications, are introduced. Furthermore, the routing process and its challenges are briefly explained in FANET. Then, a classification of reinforcement learning-based routing protocols is suggested for the flying ad hoc networks. This classification categorizes routing protocols based on the learning algorithm, the routing algorithm, and the data dissemination process. Finally, we present the existing opportunities and challenges in this field to provide a detailed and accurate view for researchers to be aware of the future research directions in order to improve the existing reinforcement learning-based routing algorithms. Full article
(This article belongs to the Section Network Science)
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Article
A Novel Early Warning Method for Handling Non-Homogeneous Information
Mathematics 2022, 10(16), 3016; https://doi.org/10.3390/math10163016 - 21 Aug 2022
Viewed by 274
Abstract
Early warnings are an indispensable part of emergency management, which is a powerful way to eliminate or reduce the negative impacts caused by emergencies in advance. Early warning problems have been discussed from different perspectives and have obtained fruitful results. Information plays a [...] Read more.
Early warnings are an indispensable part of emergency management, which is a powerful way to eliminate or reduce the negative impacts caused by emergencies in advance. Early warning problems have been discussed from different perspectives and have obtained fruitful results. Information plays a critical role in all kinds of decision problems, with no exception for the early warning problem. There are various information types related to emergencies in real-world situations; however, existing early warning studies only considered a single information type, which might not describe the problem properly and comprehensively. To enrich existing early warning studies, a novel early warning method considering non-homogeneous information together with experts’ hesitation is proposed, in which numerical values, interval values, linguistic terms, and hesitant fuzzy linguistic terms are considered. To facilitate the computations with non-homogeneous information, a transformation process needs to be conducted. On such a basis, a fuzzy TOPSIS method based on alpha-level sets is employed to handle the transformed fuzzy information due to its superiority in obtaining information and its capacity to contain as much information as possible during the early warning process. Additionally, two different options are provided to analyze the status and tendency of early warning objects. Finally, an illustrative example about early warnings about landslides and a related comparison are conducted to demonstrate the novelty, superiority, and feasibility and validity of the proposed method. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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Article
A New Robust and Secure 3-Level Digital Image Watermarking Method Based on G-BAT Hybrid Optimization
Mathematics 2022, 10(16), 3015; https://doi.org/10.3390/math10163015 - 21 Aug 2022
Viewed by 383
Abstract
This contribution applies tools from the information theory and soft computing (SC) paradigms to the embedding and extraction of watermarks in aerial remote sensing (RS) images to protect copyright. By the time 5G came along, Internet usage had already grown exponentially. Regarding copyright [...] Read more.
This contribution applies tools from the information theory and soft computing (SC) paradigms to the embedding and extraction of watermarks in aerial remote sensing (RS) images to protect copyright. By the time 5G came along, Internet usage had already grown exponentially. Regarding copyright protection, the most important responsibility of the digital image watermarking (DIW) approach is to provide authentication and security for digital content. In this paper, our main goal is to provide authentication and security to aerial RS images transmitted over the Internet by the proposal of a hybrid approach using both the redundant discrete wavelet transform (RDWT) and the singular value decomposition (SVD) schemes for DIW. Specifically, SC is adopted in this work for the numerical optimization of critical parameters. Moreover, 1-level RDWT and SVD are applied on digital cover image and singular matrices of LH and HL sub-bands are selected for watermark embedding. Further selected singular matrices SLH and SHL are split into 3×3 non-overlapping blocks, and diagonal positions are used for watermark embedding. Three-level symmetric encryption with low computational cost is used to ensure higher watermark security. A hybrid grasshopper–BAT (G-BAT) SC-based optimization algorithm is also proposed in order to achieve high quality DIW outcomes, and a broad comparison against other methods in the state-of-the-art is provided. The experimental results have demonstrated that our proposal provides high levels of imperceptibility, robustness, embedding capacity and security when dealing with DIW of aerial RS images, even higher than the state-of-the-art methods. Full article
(This article belongs to the Special Issue Mathematical Methods in Image Processing and Computer Vision)
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Article
Using Matlab/Simulink Software Package to Investigate Fault Behaviors in HVDC System
Mathematics 2022, 10(16), 3014; https://doi.org/10.3390/math10163014 - 21 Aug 2022
Viewed by 321
Abstract
Existing studies show that several performance issues will arise in the HVDC link during the three phase-to-ground fault at the side of the inverter and that the DC voltage will oscillate around zero and will not affect the rectifier of the AC system [...] Read more.
Existing studies show that several performance issues will arise in the HVDC link during the three phase-to-ground fault at the side of the inverter and that the DC voltage will oscillate around zero and will not affect the rectifier of the AC system though the inverter of the AC system, and the AC voltages will become zero and the AC currents will show high amplitude as well as minor disturbances. It has also been argued that when the fault is applied on a single-phase to ground fault at the inverter side on the AC side, the voltage will decrease. In this paper, we focus on single line-to-ground fault, double line-to-ground fault, and three phase-to-ground fault at the inverter of the AC system and their behavior on the DC link as well as on the AC system of the rectifier with detailed simulations. A high voltage direct current (HVDC) Monopolar system is modeled using a Matlab/Simulink software package for the research. The results show that during the three phase-to-ground fault at the AC system of the inverter, the DC voltage will increase with a bogus waveform and the currents of the AC system at the rectifier will collapse to zero.At the double phase-to-ground fault level, the DC voltage will experience an increase in waveform while the currents of the AC system of the rectifier will experience different disturbances. At the single phase-to-ground fault level, the DC voltage will remain stable and the rectifier side of the AC system will also experience a stable state for both currents and voltages. Full article
(This article belongs to the Special Issue Modeling and Simulation for the Electrical Power System)
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Article
Insight into Dynamic of Mono and Hybrid Nanofluids Subject to Binary Chemical Reaction, Activation Energy, and Magnetic Field through the Porous Surfaces
Mathematics 2022, 10(16), 3013; https://doi.org/10.3390/math10163013 - 21 Aug 2022
Cited by 2 | Viewed by 298
Abstract
The mathematical modeling of the activation energy and binary chemical reaction system with six distinct types of nanoparticles, along with the magnetohydrodynamic effect, is studied in this paper. Different types of hybrid nanofluids flowing over porous surfaces with heat and mass transfer aspects [...] Read more.
The mathematical modeling of the activation energy and binary chemical reaction system with six distinct types of nanoparticles, along with the magnetohydrodynamic effect, is studied in this paper. Different types of hybrid nanofluids flowing over porous surfaces with heat and mass transfer aspects are examined here. The empirical relations for nanoparticle materials associated with thermophysical properties are expressed as partial differential equations, which are then interpreted into ordinary differential expressions using appropriate variables. The initial shooting method converts the boundary condition into the initial condition with an appropriate guess and finally finds out an accurate numerical solution by using the Runge–Kutta method with numerical stability. Variations in nanoparticle volume fraction at the lower and upper walls of porous surfaces, as well as the heat transfer rate measurements, are computed using the controlling physical factors. The effects of the flow-related variables on the axial velocity, radial velocity, temperature, and concentration profile dispersion are also investigated. The Permeable Reynolds number is directly proportional to the regression parameter. The injection/suction phenomenon associated with the expanding/contracting cases, respectively, have been described with engineering parameters. The hybrid nanoparticle volume fraction (1–5%) has a significant effect on the thermal system and radial velocity. Full article
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Article
On Hermite Functions, Integral Kernels, and Quantum Wires
Mathematics 2022, 10(16), 3012; https://doi.org/10.3390/math10163012 - 21 Aug 2022
Viewed by 311
Abstract
In this note, we first evaluate and subsequently achieve a rather accurate approximation of a scalar product, the calculation of which is essential in order to determine the ground state energy in a two-dimensional quantum model. This scalar product involves an integral operator [...] Read more.
In this note, we first evaluate and subsequently achieve a rather accurate approximation of a scalar product, the calculation of which is essential in order to determine the ground state energy in a two-dimensional quantum model. This scalar product involves an integral operator defined in terms of the eigenfunctions of the harmonic oscillator, expressed in terms of the well-known Hermite polynomials, so that some rather sophisticated mathematical tools are required. Full article
(This article belongs to the Special Issue Applications of Functional Analysis in Quantum Physics)
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Article
Reliability Assessment of an Unscented Kalman Filter by Using Ellipsoidal Enclosure Techniques
Mathematics 2022, 10(16), 3011; https://doi.org/10.3390/math10163011 - 21 Aug 2022
Viewed by 392
Abstract
The Unscented Kalman Filter (UKF) is widely used for the state, disturbance, and parameter estimation of nonlinear dynamic systems, for which both process and measurement uncertainties are represented in a probabilistic form. Although the UKF can often be shown to be more reliable [...] Read more.
The Unscented Kalman Filter (UKF) is widely used for the state, disturbance, and parameter estimation of nonlinear dynamic systems, for which both process and measurement uncertainties are represented in a probabilistic form. Although the UKF can often be shown to be more reliable for nonlinear processes than the linearization-based Extended Kalman Filter (EKF) due to the enhanced approximation capabilities of its underlying probability distribution, it is not a priori obvious whether its strategy for selecting sigma points is sufficiently accurate to handle nonlinearities in the system dynamics and output equations. Such inaccuracies may arise for sufficiently strong nonlinearities in combination with large state, disturbance, and parameter covariances. Then, computationally more demanding approaches such as particle filters or the representation of (multi-modal) probability densities with the help of (Gaussian) mixture representations are possible ways to resolve this issue. To detect cases in a systematic manner that are not reliably handled by a standard EKF or UKF, this paper proposes the computation of outer bounds for state domains that are compatible with a certain percentage of confidence under the assumption of normally distributed states with the help of a set-based ellipsoidal calculus. The practical applicability of this approach is demonstrated for the estimation of state variables and parameters for the nonlinear dynamics of an unmanned surface vessel (USV). Full article
(This article belongs to the Special Issue Set-Based Methods for Differential Equations and Applications)
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Article
Algebraic Construction of the Sigma Function for General Weierstrass Curves
Mathematics 2022, 10(16), 3010; https://doi.org/10.3390/math10163010 - 20 Aug 2022
Viewed by 318
Abstract
The Weierstrass curve X is a smooth algebraic curve determined by the Weierstrass canonical form, [...] Read more.
The Weierstrass curve X is a smooth algebraic curve determined by the Weierstrass canonical form, yr+A1(x)yr1+A2(x)yr2++Ar1(x)y+Ar(x)=0, where r is a positive integer, and each Aj is a polynomial in x with a certain degree. It is known that every compact Riemann surface has a Weierstrass curve X, which is birational to the surface. The form provides the projection ϖr:XP as a covering space. Let RX:=H0(X,OX()) and RP:=H0(P,OP()). Recently, we obtained the explicit description of the complementary module RXc of RP-module RX, which leads to explicit expressions of the holomorphic form except , H0(P,AP()) and the trace operator pX such that pX(P,Q)=δP,Q for ϖr(P)=ϖr(Q) for P,QX\{}. In terms of these, we express the fundamental two-form of the second kind Ω and its connection to the sigma function for X. Full article
(This article belongs to the Special Issue Partial Differential Equations and Applications)
Article
Adaptive Barrier Fast Terminal Sliding Mode Actuator Fault Tolerant Control Approach for Quadrotor UAVs
Mathematics 2022, 10(16), 3009; https://doi.org/10.3390/math10163009 - 20 Aug 2022
Cited by 1 | Viewed by 310
Abstract
This paper proposes an adaptive barrier fast terminal sliding mode control (ABFTSMC) approach for quadrotor unmanned aerial vehicles (UAV). Its main objectives are to mitigate the external disturbances, parametric uncertainties, and actuator faults. An adaptive barrier function is considered in the design to [...] Read more.
This paper proposes an adaptive barrier fast terminal sliding mode control (ABFTSMC) approach for quadrotor unmanned aerial vehicles (UAV). Its main objectives are to mitigate the external disturbances, parametric uncertainties, and actuator faults. An adaptive barrier function is considered in the design to ensure the finite-time convergence of the output variables to a predefined locality of zero, independent of the disturbance bounds. A fast terminal sliding mode control (FTSMC) approach is designed to speed up the convergence rate in both reaching and sliding phases. The design considers hyperbolic tangent functions in the adaptive control law to drastically reduce the chattering effect, typically associated with the standard SMC. The performance of the proposed approach was assessed using a quadrotor UAV subject to external disturbances and sudden actuator faults. The obtained results show that the trajectory and the sliding surface converge to the origin in a finite time, without being affected by the high disturbance and actuator faults. In this method, due to the substitution of the discontinuous function by the hyperbolic tangent function, the chattering effect has also been highly reduced. Full article
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Article
Risk Propagation and Supply Chain Health Control Based on the SIR Epidemic Model
Mathematics 2022, 10(16), 3008; https://doi.org/10.3390/math10163008 - 20 Aug 2022
Viewed by 331
Abstract
Risk propagation is occurring as an exceptional challenge to supply chain management. Identifying which supplier has the greater possibility of interruptions is pivotal for managing the occurrence of these risks, which have a significant impact on the supply chain. Identifying and predicting how [...] Read more.
Risk propagation is occurring as an exceptional challenge to supply chain management. Identifying which supplier has the greater possibility of interruptions is pivotal for managing the occurrence of these risks, which have a significant impact on the supply chain. Identifying and predicting how these risks propagate and understanding how these risks dynamically diffuse if control strategies are installed can help to better manage supply chain risks. Drawing on the complex systems and epidemiological literature, we research the impact of the global supply network structure on risk propagation and supply network health. The SIR model is used to dynamically identify and predict the risk status of the supply chain risk at different times. The results show that there is a significant relationship between network structure and risk propagation and supply network health. We demonstrate the importance of supply network visibility and of the extraction of the information of node firms. We build up an R package for geometric graphs and epidemics. This paper applies the R package to model the supply chain risk for an automotive manufacturing company. The R package provides a firm to construct the complicated interactions among suppliers and display how these interactions impact on risks. Theoretically, our study adapts a computational approach to contribute to the understanding of risk management and supply networks. Managerially, our study demonstrates how the supply chain network analysis approach can benefit the managers by developing a more holistic framework of system-wide risk propagation. This provides guidance for network governance policies, which will lead to healthier supply chains. Full article
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Article
Pseudo General Overlap Functions and Weak Inflationary Pseudo BL-Algebras
Mathematics 2022, 10(16), 3007; https://doi.org/10.3390/math10163007 - 20 Aug 2022
Cited by 1 | Viewed by 275
Abstract
General overlap functions are generalized on the basis of overlap functions, which have better application effects in classification problems, and the (weak) inflationary BL-algebras as the related algebraic structure were also studied. However, general overlap functions are a class of aggregation operators, and [...] Read more.
General overlap functions are generalized on the basis of overlap functions, which have better application effects in classification problems, and the (weak) inflationary BL-algebras as the related algebraic structure were also studied. However, general overlap functions are a class of aggregation operators, and their commutativity puts certain restrictions on them. In this article, we first propose the notion of pseudo general overlap functions as a non-commutative generalization of general overlap functions, so as to extend their application range, then illustrate their relationship with several other commonly used aggregation functions, and characterize some construction methods. Secondly, the residuated implications induced by inflationary pseudo general overlap functions are discussed, and some examples are given. Then, on this basis, we show the definitions of inflationary pseudo general residuated lattices (IPGRLs) and weak inflationary pseudo BL-algebras, and explain that the weak inflationary pseudo BL-algebras can be gained by the inflationary pseudo general overlap functions. Moreover, they are more extensive algebraic structures, thus enriching the content of existing non-classical logical algebra. Finally, their related properties and their relations with some algebraic structures such as non-commutative residuated lattice-ordered groupoids are investigated. The legend reveals IPGRLs include all non-commutative algebraic structures involved in the article. Full article
(This article belongs to the Special Issue FSTA: Fuzzy Set Theory and Applications)
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Article
New Tilt Fractional-Order Integral Derivative with Fractional Filter (TFOIDFF) Controller with Artificial Hummingbird Optimizer for LFC in Renewable Energy Power Grids
Mathematics 2022, 10(16), 3006; https://doi.org/10.3390/math10163006 - 20 Aug 2022
Viewed by 328
Abstract
Recent advancements in renewable generation resources and their vast implementation in power sectors have posed serious challenges regarding their operation, protection, and control. Maintaining operating frequency at its nominal value and reducing tie-line power deviations represent crucial factors for these advancements due to [...] Read more.
Recent advancements in renewable generation resources and their vast implementation in power sectors have posed serious challenges regarding their operation, protection, and control. Maintaining operating frequency at its nominal value and reducing tie-line power deviations represent crucial factors for these advancements due to continuous reduction of power system inertia. In this paper, a new modified load frequency controller (LFC) method is proposed based on fractional calculus combinations. The tilt fractional-order integral-derivative with fractional-filter (TFOIDFF) is proposed in this paper for LFC applications. The proposed TFOIDFF controller combines the benefits of tilt, FOPID, and fractional filter regulators. Furthermore, a new application is introduced based on the recently presented artificial hummingbird optimizer algorithm (AHA) for simultaneous optimization of the proposed TFOIDFF parameters in the studied two-area power grids. The contribution of electric vehicle (EVs) is considered in the centralized control strategy using the proposed TFOIDFF controller. The performance of the proposed TFOIDFF controller has been compared with the existing tilt with filter, PID with filter, FOPID with filter and hybrid fractional-order with filter LFCs from the literature. Moreover, the AHA optimizer results are compared with the featured LFC optimization algorithms in the literature. The proposed TFOIDFF and AHA optimizer are validated against renewable energy fluctuations, load stepping, generation/loading uncertainty, and power-grid parameter uncertainty. The AHA optimizer is compared with the widely-used optimizers in the literature, including the PSO, ABC, BOA, and AEO optimizers at the IAE, ISE, ITAE, and ITSE objectives. For instance, the proposed AHA method has a minimized IAE after 34 iterations of 0.03178 compared to 0.03896 with PSO, 0.04548 with AEO, 0.04812 with BOA, and 0.05483 with ABC optimizer. Therefore, fast and better minimization of objective functions are achieved using the proposed AHA method. Full article
(This article belongs to the Special Issue Systems Modeling, Analysis and Optimization)
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Article
Gain-Scheduled Sliding-Mode-Type Iterative Learning Control Design for Mechanical Systems
Mathematics 2022, 10(16), 3005; https://doi.org/10.3390/math10163005 - 20 Aug 2022
Viewed by 300
Abstract
In this paper, a novel gain-scheduled sliding-mode-type (SM-type) iterative learning (IL) control approach is proposed for the high-precision trajectory tracking of mechanical systems subject to model uncertainties and disturbances. Based on the SM variable, the proposed controller is synthesized involving a feedback regulation [...] Read more.
In this paper, a novel gain-scheduled sliding-mode-type (SM-type) iterative learning (IL) control approach is proposed for the high-precision trajectory tracking of mechanical systems subject to model uncertainties and disturbances. Based on the SM variable, the proposed controller is synthesized involving a feedback regulation item, a feedforward learning item, and a robust switching item. The feedback regulation item is adopted to regulate the position and velocity tracking errors, the feedforward learning item is applied to handle the model uncertainties and repetitive disturbance, and the robust switching item is introduced to compensate the nonrepetitive disturbance and linearization residual error. Moreover, the gain-scheduled mechanism is employed for both the feedback regulation item and feedforward learning item to enhance the convergence speed. Convergence analysis illustrates that the position and velocity tracking errors can eventually regulate to zero under the proposed controller. By combining the advantages of both SM control and IL control, the proposed controller has strong robustness against model uncertainties and disturbances. Lastly, simulations and comparisons are provided to evaluate the efficiency and excellent performance of the proposed control approach. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
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Article
Statistical Modeling on the Severity of Unhealthy Air Pollution Events in Malaysia
Mathematics 2022, 10(16), 3004; https://doi.org/10.3390/math10163004 - 20 Aug 2022
Viewed by 324
Abstract
This study proposes the concept of severity as an alternative measure of extreme air pollution events. Information about severity can be derived from the cumulative effect of air pollution events, which can be determined from unhealthy Air Pollution Index (API) values that occur [...] Read more.
This study proposes the concept of severity as an alternative measure of extreme air pollution events. Information about severity can be derived from the cumulative effect of air pollution events, which can be determined from unhealthy Air Pollution Index (API) values that occur for a consecutive period. On the basis of the severity, an analysis of extreme air pollution events can be obtained through the application of the generalized extreme-value (GEV) model. A case study was conducted using hourly API data in Klang, Malaysia, from 1 January 1997 to 31 August 2020. The block-maxima approach was integrated with information about monsoon seasons to determine suitable data points for GEV modeling. Based on the GEV model, the estimated severity levels corresponding to their return periods are determined. The results reveal that pollution severity in Klang tends to rise with increases in the length of return periods that are measured based on seasonal monsoons as a temporal scale. In conclusion, the return period for severity provides a good basis for measuring the risk of recurrence of extreme pollution events. Full article
(This article belongs to the Special Issue Statistical Models in the Era of Big Data)
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Article
Quantifying Intra-Catchment Streamflow Processes and Response to Climate Change within a Climatic Transitional Zone: A Case Study of Buffalo Catchment, Eastern Cape, South Africa
Mathematics 2022, 10(16), 3003; https://doi.org/10.3390/math10163003 - 19 Aug 2022
Viewed by 257
Abstract
The complexity of streamflow processes inhibits significant information about catchment performance and its sensitivity to climate change. Little is known about the severity of climate change within the coastal area of the monsoon–subtropical zone of climatic transition. This study advances a quasi-local scale [...] Read more.
The complexity of streamflow processes inhibits significant information about catchment performance and its sensitivity to climate change. Little is known about the severity of climate change within the coastal area of the monsoon–subtropical zone of climatic transition. This study advances a quasi-local scale analysis to simplify daily streamflow dynamics and their relationship with monthly hydro-climatic series (1981–2020) using six gauging stations on the Buffalo River due to its socio-economic significance. An integrated framework based on continuous wavelet transform (CWT), wavelet coherence (WC), innovative trend analysis (ITA), Mann–Kendall (MK), Sequential Mann–Kendall, and Pettitt tests were employed. CWT showed huge declivity in daily streamflow intensity (7676 to 719), >100 mm/day streamflow frequency (15 to 0), and wetness spell time-gap. WC obtained significant streamflow–rainfall co-movement of 8–196-month periodicities, which characterized Buffalo as anti-phase (1–4-month), lag-lead (8–32-month), and in-phase (64–196-month) in processes. The Buffalo River’s sensitivity to significantly decreasing rainfall trends and increasing temperature trends depicts Streamflow–ENSO teleconnection. Contrarily, ITA and MK exhibited significantly increasing trends of tributaries’ low flow and inferred the perennial status of the catchment. The Pettitt test corroborates the deductions and asserts 1990 (temperature), 1996 (streamflow), and 2004/2013 (rainfall) as the abrupt change points, while SMK captured a critical streamflow slump in 2015–2020. Overall, the study proved the reductionist approach and model framework to achieve the hydrological process simplification and resolution of hotspots of hydrologic extremes within a bimodal climate with complex topography. This study remarks on the management policy of the BR and provides a reference for managing water resources and catchment hydro-climatic extremes. Full article
(This article belongs to the Special Issue Advanced Statistical Techniques in Oceans and Climate Research)
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Article
Solution of the Thermoelastic Problem for a Two-Dimensional Curved Beam with Bimodular Effects
Mathematics 2022, 10(16), 3002; https://doi.org/10.3390/math10163002 - 19 Aug 2022
Viewed by 246
Abstract
In classical thermoelasticity, the bimodular effect of materials is rarely considered. However, all materials will present, in essence, different properties in tension and compression, more or less. The bimodular effect is generally ignored only for simple analysis. In this study, we theoretically analyze [...] Read more.
In classical thermoelasticity, the bimodular effect of materials is rarely considered. However, all materials will present, in essence, different properties in tension and compression, more or less. The bimodular effect is generally ignored only for simple analysis. In this study, we theoretically analyze a two-dimensional curved beam with a bimodular effect and under mechanical and thermal loads. We first establish a simplified model on a subarea in tension and compression. On the basis of this model, we adopt the Duhamel similarity theorem to change the initial thermoelastic problem as an elasticity problem without the thermal effect. The superposition of the special solution and supplement solution of the Lamé displacement equation enables us to satisfy the boundary conditions and stress continuity conditions of the bimodular curved beam, thus obtaining a two-dimensional thermoelastic solution. The results indicate that the solution obtained can reduce to bimodular curved beam problems without thermal loads and to the classical Golovin solution. In addition, the bimodular effect on thermal stresses is discussed under linear and non-linear temperature rise modes. Specially, when the compressive modulus is far greater than the tensile modulus, a large compressive stress will occur at the inner edge of the curved beam, which should be paid with more attention in the design of the curved beams in a thermal environment. Full article
(This article belongs to the Special Issue Applied Mathematics and Continuum Mechanics)
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Article
A Generalized Linear Joint Trained Framework for Semi-Supervised Learning of Sparse Features
Mathematics 2022, 10(16), 3001; https://doi.org/10.3390/math10163001 - 19 Aug 2022
Viewed by 221
Abstract
The elastic net is among the most widely used types of regularization algorithms, commonly associated with the problem of supervised generalized linear model estimation via penalized maximum likelihood. Its attractive properties, originated from a combination of 1 and 2 norms, endow [...] Read more.
The elastic net is among the most widely used types of regularization algorithms, commonly associated with the problem of supervised generalized linear model estimation via penalized maximum likelihood. Its attractive properties, originated from a combination of 1 and 2 norms, endow this method with the ability to select variables, taking into account the correlations between them. In the last few years, semi-supervised approaches that use both labeled and unlabeled data have become an important component in statistical research. Despite this interest, few researchers have investigated semi-supervised elastic net extensions. This paper introduces a novel solution for semi-supervised learning of sparse features in the context of generalized linear model estimation: the generalized semi-supervised elastic net (s2net), which extends the supervised elastic net method, with a general mathematical formulation that covers, but is not limited to, both regression and classification problems. In addition, a flexible and fast implementation for s2net is provided. Its advantages are illustrated in different experiments using real and synthetic data sets. They show how s2net improves the performance of other techniques that have been proposed for both supervised and semi-supervised learning. Full article
(This article belongs to the Special Issue Applied and Methodological Data Science)
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Article
A Non-Invasive Method to Evaluate Fuzzy Process Capability Indices via Coupled Applications of Artificial Neural Networks and the Placket–Burman DOE
Mathematics 2022, 10(16), 3000; https://doi.org/10.3390/math10163000 - 19 Aug 2022
Viewed by 241
Abstract
The capability analysis of a process against requirements is often an instrument of change. The traditional and fuzzy process capability approaches are the most useful statistical techniques for determining the intrinsic spread of a controlled process for establishing realistic specifications and use for [...] Read more.
The capability analysis of a process against requirements is often an instrument of change. The traditional and fuzzy process capability approaches are the most useful statistical techniques for determining the intrinsic spread of a controlled process for establishing realistic specifications and use for comparative processes. In the industry, the traditional approach is the most commonly used instrument to assess the impact of continuous improvement projects. However, these methods used to evaluate process capability indices could give misleading results because the dataset employed corresponds to the final product/service measures. This paper reviews an alternative procedure to assess the fuzzy process capability indices based on the statistical methodology involved in the modeling and design of experiments. Firstly, a model with reasonable accuracy is developed using a neural network approach. This model is embedded in a graphic user interface (GUI). Using the GUI, an experimental design is carried out, first to know the membership function of the process variability and then include this variability in the model. Again, an experimental design identifies the improved operating conditions for the significative independent variables. A new dataset is generated with these operating conditions, including the minimum error reached for each independent variable. Finally, the GUI is used to get a new prediction for the response variable. The fuzzy process capability indices are determined using the triangular membership function and the predicted response values. The feasibility of the proposed method was validated using a random data set corresponding to the basis weight of a papermaking process. The results indicate that the proposed method provides a better overview of the process performance, showing its true potential. The proposed method can be considered non-invasive. Full article
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Article
Tourist Arrival Forecasting Using Multiscale Mode Learning Model
Mathematics 2022, 10(16), 2999; https://doi.org/10.3390/math10162999 - 19 Aug 2022
Viewed by 229
Abstract
The forecasting of tourist arrival depends on the accurate modeling of prevalent data patterns found in tourist arrival, especially for daily tourist arrival, where tourist arrival changes are more complex and highly nonlinear. In this paper, a new multiscale mode learning-based tourist arrival [...] Read more.
The forecasting of tourist arrival depends on the accurate modeling of prevalent data patterns found in tourist arrival, especially for daily tourist arrival, where tourist arrival changes are more complex and highly nonlinear. In this paper, a new multiscale mode learning-based tourist arrival forecasting model is proposed to exploit different multiscale data features in tourist arrival movement. Two popular Mode Decomposition models (MD) and the Convolutional Neural Network (CNN) model are introduced to model the multiscale data features in the tourist arrival data The data patterns at different scales are extracted using these two different MD models which dynamically decompose tourist arrival into the distinctive intrinsic mode function (IMF) data components. The convolutional neural network uses the deep network to further model the multiscale data structure of tourist arrivals, with the reduced dimensionality of key multiscale data features and finer modeling of nonlinearity in tourist arrival. Our empirical results using daily tourist arrival data show that the MD-CNN tourist arrival forecasting model significantly improves the forecasting reliability and accuracy. Full article
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